Affine spaces and maps

The definitions are worked out of the presentation of Andrew D. Lewis, that is to say
chapter 1 of
Lagrangian Mechanics, Dynamics, and Control. The designation selbst-affin (= self-affin) was chosen by myself as a makeshift to give a name to this thing. It is expressly pointed out that this is not a common notation that you can make further use of thoughtlessly and without explanation.